Sequential Change-Point Detection and Estimation

Abstract

Two groups of sequential testing procedures are proposed to detect an abrupt change in the distribution of a sequence of observations: truncated and open ended. They are based on large sample strong approximations of the efficient score vector under the null hypothesis of no change and under the alternative hypothesis. An estimator of the time of change is proposed and its approximate bias is analyzed. The estimation of the new parameters that describe the changed distribution naturally follows.

Keywords:

• Sequential tests
• Change detection
• Strong approximations
• Efficient score vector
• Exponential family